Parametric instability of a cantilevered column under periodic loads in the direction of the tangency coefficient

1995 ◽  
Vol 183 (2) ◽  
pp. 253-267 ◽  
Author(s):  
C.-C. Chen ◽  
M.-K. Yeh
Keyword(s):  
Parametric Instability

scholarly journals Parametric instability in a free-evolving warped protoplanetary disc

2020 ◽  
Vol 500 (3) ◽  
pp. 4248-4256
Author(s):  
Hongping Deng ◽  
Gordon I Ogilvie ◽  
Lucio Mayer
Keyword(s):  
Wave Equations ◽  
Hydrodynamic Instability ◽  
Parametric Instability ◽  
Low Viscosity ◽  
Crossing Time ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
First Time ◽  
Bending Wave ◽  
Grid Based

ABSTRACT Warped accretion discs of low viscosity are prone to hydrodynamic instability due to parametric resonance of inertial waves as confirmed by local simulations. Global simulations of warped discs, using either smoothed particle hydrodynamics or grid-based codes, are ubiquitous but no such instability has been seen. Here, we utilize a hybrid Godunov-type Lagrangian method to study parametric instability in global simulations of warped Keplerian discs at unprecedentedly high resolution (up to 120 million particles). In the global simulations, the propagation of the warp is well described by the linear bending-wave equations before the instability sets in. The ensuing turbulence, captured for the first time in a global simulation, damps relative orbital inclinations and leads to a decrease in the angular momentum deficit. As a result, the warp undergoes significant damping within one bending-wave crossing time. Observed protoplanetary disc warps are likely maintained by companions or aftermath of disc breaking.

Temporal Evolution of a Three-Wave Parametric Instability

1973 ◽  
Vol 31 (19) ◽  
pp. 1190-1193 ◽  
Author(s):  
M. N. Rosenbluth ◽  
R. B. White ◽  
C. S. Liu
Keyword(s):  
Temporal Evolution ◽  
Parametric Instability

scholarly journals Parametric Instability Rates in Periodically Driven Band Systems

2017 ◽  
Vol 7 (2) ◽  
Author(s):  
S. Lellouch ◽  
M. Bukov ◽  
E. Demler ◽  
N. Goldman
Keyword(s):  
Parametric Instability ◽  
Periodically Driven

scholarly journals Parametric Instability of a Traveling Plate Partially Supported by a Laterally Moving Elastic Foundation

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
V. Kartik ◽  
J. A. Wickert
Keyword(s):  
Data Storage ◽  
Parametric Instability ◽  
Primary Resonance ◽  
Free Edge ◽  
Moving Plate ◽  
Torsional Mode ◽  
Plane Vibration ◽  
Out Of Plane ◽  
Axially Moving ◽  
The Stability

The parametric excitation of an axially moving plate is examined in an application where a partial foundation moves in the plane of the plate and in a direction orthogonal to the plate’s transport. The stability of the plate’s out-of-plane vibration is of interest in a magnetic tape data storage application where the read/write head is substantially narrower than the tape’s width and is repositioned during track-following maneuvers. In this case, the model’s equation of motion has time-dependent coefficients, and vibration is excited both parametrically and by direct forcing. The parametric instability of out-of-plane vibration is analyzed by using the Floquet theory for finite values of the foundation’s range of motion. For a relatively soft foundation, vibration is excited preferentially at the primary resonance of the plate’s fundamental torsional mode. As the foundation’s stiffness increases, multiple primary and combination resonances occur, and they dominate the plate’s stability; small islands, however, do exist within unstable zones of the frequency-amplitude parameter space for which vibration is marginally stable. The plate’s and foundation’s geometry, the foundation’s stiffness, and the excitation’s amplitude and frequency can be selected in order to reduce undesirable vibration that occurs along the plate’s free edge.

In-Plane Parametric Vibrations of Curved Bellows Subjected to Oscillating Internal Fluid Pressure Excitation

2004 ◽  
Author(s):  
Masahiro Watanabe ◽  
Eiji Tachibana ◽  
Nobuyuki Kobayashi
Keyword(s):  
Stability Analysis ◽  
Natural Frequencies ◽  
Parametric Instability ◽  
Fluid Pressure ◽  
Parametric Vibrations ◽  
Internal Fluid ◽  
Mathieu’S Equation ◽  
Stability Maps ◽  
Plane Direction ◽  
Pressure Excitation

This paper deals with the theoretical stability analysis of in-plane parametric vibrations of a curved bellows subjected to periodic internal fluid pressure excitation. The curved bellows studied in this paper are fixed at both ends rigidly, and are excited by the periodic internal fluid pressure. In the theoretical stability analysis, the governing equation of the curved bellows subjected to periodic internal fluid pressure excitation is derived as a Mathieu’s equation by using finite element method (FEM). Natural frequencies of the curved bellows are examined and stability maps are presented for in-plane parametric instability. It is found that the natural frequencies of the curved bellows decrease with increasing the static internal fluid pressure and buckling occurs due to high internal fluid pressure. It is also found that two types of parametric vibrations, longitudinal and transverse vibrations, occur to the curved bellows in-plane direction due to the periodic internal fluid pressure excitation. Moreover, effects of axis curvature on the parametric instability regions are examined theoretically.

Parametric Instability in Metallic Bellows Subjected to Seismic Excitation

2010 ◽  
Author(s):  
Nobuyuki Kobayashi ◽  
Keisaku Kitada ◽  
Yoshiki Sugawara
Keyword(s):  
Parametric Instability ◽  
Fluid Pressure ◽  
Element Model ◽  
Frequency Component ◽  
Seismic Excitation ◽  
Axial Stiffness ◽  
Predominant Frequency ◽  
Earthquake Motion ◽  
Static Fluid ◽  
Stiffness Variation

This paper investigates the parametric instability of a metallic bellows filled with fluid and subjected to the variance of dynamic internal pressure due to an earthquake. The axial stiffness of the bellows varies due to the variation in internal static fluid pressure, and this stiffness variation induces a parametric instability in the bellows. A finite element model describing a bellows connected to a pipe is developed to examine the question of whether parametric instability is excited in such bellows by earthquake motion, which is not the harmonic vibration. Numerical simulations and experiments were carried out using the acceleration recorded by past recorded actual earthquakes. We find that indeed parametric instability may appear in the bellows when the natural frequency of the pipe is close to the predominant frequency component of the earthquake, though the earthquake motion is not harmonic.

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